student test scre is a mean of 100 Aproximate normal distrib

student test scre is a mean of 100 Aproximate normal distribution is 10 the 25 th percentile is 93 the 75 th percentile is ? How do I find the z score?

Solution

The percentile represents the area in the normal distribution to the left of the normal distribution curve.

25 percentile means the data more than 25%of the total data.

For the percentile of 25% it means that .25 of the area is left to the normal distribution curve.Using the z table the z score corresponding to the p value of .25 is -.6745

Similarly for the 75th percentile the area to the left of the normal distribution curve is .75.Using the z table the z score corresponding to the p value of .75 is .6745

If the mean of the normal distribution is k then the 75th percentile is k+(k-93)=2k-93

Here the mean is =100

The 75th percentile is 2*100-93 =107